A boat sails directly toward a $$ 300-\mathrm{m} $$ skyscraper that stands on the edge of a harbor. The angular size of the building is the angle formed by lines from the top and bottom of the building to the observer (see figure). Complete parts a and $$ b $$ below. a. Use a trigonometric equation to find an expression for the angle, $$ heta $$, in terms of x . (Type an equation.) b. What is the rate of change of the angular size, $$ \frac{\mathrm{d} heta}{\mathrm{dx}} $$, when the boat is $$ \mathrm{x}=350 \mathrm{~m} $$ from the building? rad/m (Round to five decimal places as needed.)

Question

A boat sails directly toward a $$ 300-\mathrm{m} $$ skyscraper that stands on the edge of a harbor. The angular size of the building is the angle formed by lines from the top and bottom of the building to the observer (see figure). Complete parts a and $$ b $$ below. a. Use a trigonometric equation to find an expression for the angle, $$ 	heta $$, in terms of x . (Type an equation.) b. What is the rate of change of the angular size, $$ \frac{\mathrm{d} 	heta}{\mathrm{dx}} $$, when the boat is $$ \mathrm{x}=350 \mathrm{~m} $$ from the building? rad/m (Round to five decimal places as needed.)

UpStudy AI · Accepted Answer

a. $$	heta = 	an^{-1}\left(\frac{300}{x}ight)$$ b. $$\frac{d	heta}{dx} \approx -0.00141 \, 	ext{rad/m}$$

UpStudy ThothAI Solution

Quick Answer

Step-by-step Solution

UpStudy ThothAI Solution

Quick Answer

Step-by-step Solution

Related Questions